How to extract stat_smooth exponential fit parameters ggplot2

Question

I've already tried many of the suggestions found here, but I simply can't figure it out.

Is it possible to extract the equation (y = a+exp(-b*x)) from a line fitted with stat_smooth?

This is a data example:

df <-data_frame(Time = c(0.5,1,2,4,8,16,24), Concentration = c(1,0.5,0.2,0.05,0.02,0.01,0.001))


Plot <- ggplot(df, aes(x=Time, y=Concentration))+
  geom_point(size=2) + 
  stat_smooth(method = nls, formula = y ~ a*exp(-b *x), 
             se = FALSE, 
              method.args = list(start = c(a=10, b=0.01)))+
  theme_classic(base_size = 15) +
  labs(x=expression(Time (h)),
       y=expression(C[t]/C[0]))

I tried to use "stat_regline_equation" , but it does not work when I add the exponential function.

Answer 1

To extract data from ggplot you can use: ggplot_build()

Values from stat_smooth() are in ggplot_build(Plot)$data[[2]]

You can assign it to the object: build <- ggplot_build(Plot)$data[[2]]

Both codes below give the same result

Plot <- ggplot(df, aes(x=Time, y=Concentration)) + geom_point(size=2) + 
  stat_smooth(method = nls, formula = y ~ a*exp(-b *x), se = FALSE, 
  method.args = list(start = c(a=10, b=0.01)))

and

Plot <- ggplot(df, aes(x=Time, y=Concentration)) + geom_point(size=2) + 
  geom_line(data=build,aes(x=x,y=y),color="blue") 

Answer 2

I don't think it's possible. (1) I poked around in the guts of the object generated by ggplot_build(Plot) and didn't find anything likely (that doesn't prove it isn't there but...) (2) If you poke around in the source code of the ggpubr::stat_regline_equation() function you can see that rather than poke around in the stored information from the smooth it has to call a package function that re-fits the linear model so it can extract the coefficients and construct the equation.

You probably just have to re-fit the model yourself:

nls_fit <- nls(formula = Concentration ~ a*exp(-b *Time), 
               start = c(a=10, b=0.01), data = df)
coef(nls_fit)

(You might find the format returned by broom::tidy(nls_fit) convenient.)

For this particular model you can also get the coefficients via

cc <- coef(glm(Concentration ~ Time, data = df, family = gaussian(link= "log")))
c(exp(cc[1]), -cc[2])

You could in principle write your own stat_ function mirroring stat_regline_equation that would encapsulate this functionality, but it would be a lot more work/wouldn't be worth it unless you were doing this operation very routinely or wanted to make it easy for others to do ...